Aerodynamics
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Lecture Notes on Classical Mechanics (A Work in Progress)
Daniel Arovas Department of Physics University of California, San Diego May 8, 2013
Contents
0.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1 1 1 2 3 3 4 5 6 6 7 8 9 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 14 15
0 Reference Materials 0.1 0.2 0.3 Lagrangian Mechanics (mostly) . . . . . . . . . . . . . . . . . . . . . . . . . Hamiltonian Mechanics (mostly) . . . . . . . . . . . . . . . . . . . . . . . . Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction to Dynamics 1.1 Introduction and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 1.1.2 1.2 Newton’s laws of motion . . . . . . . . . . . . . . . . . . . . . . . . Aside : inertial vs. gravitational mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Examples of Motion in One Dimension 1.2.1 1.2.2 1.2.3 1.2.4
Uniform force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uniform force with linear frictional damping . . . . . . . . . . . . . Uniform force with quadratic frictional damping . . . . . . . . . . . Crossed electric and magnetic fields . . . . . . . . . . . . . . . . . .
1.3
Pause for Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Systems of Particles 2.1 2.2 Work-Energy Theorem
Conservative and Nonconservative Forces . . . . . . . . . . . . . . . . . . . 2.2.1 Example : integrating F = −∇U . . . . . . . . . . . . . . . . . . .
2.3
Conservative Forces in Many Particle Systems . . . . . . . . . . . . . . . . i
ii
CONTENTS
2.4 2.5
Linear and Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . Scaling of Solutions for Homogeneous Potentials . . . . . . . . . . . . . . . 2.5.1 2.5.2 Euler’s theorem for homogeneous functions . . . . . . . . . . . . . . Scaled equations of motion . . . . . ....
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